1 = 0.999

1 = 0.99999

Algebraic proof -

Let's say x = 0.999999(infinitely)

1 = x (Start with an assumption)

10 = 10x

10 - 1 = 10x - x =9.9999(infinitely) - 0.99999(infinitely) = 9

9 = 9

We haven't reached a Reductio Ad Absurdum so our assumption must have been true, which means that

1=0.99(Infinitely)\boxed{1 = 0.99(Infinitely)}

Note by A Former Brilliant Member
4 months, 1 week ago

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1 vote

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Comments

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Hahaha! Check out this problem :-)

Páll Márton (no activity) - 4 months, 1 week ago

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Vinayak used the same Logic. :)

A Former Brilliant Member - 4 months, 1 week ago

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Yeah. What about my solution?

Páll Márton (no activity) - 4 months, 1 week ago

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@Páll Márton (no activity) Nice, I never thought of the infinite series like that. Awesome!!

A Former Brilliant Member - 4 months, 1 week ago

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@Páll Márton (no activity) I upvoted!! :-)

A Former Brilliant Member - 4 months, 1 week ago

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@A Former Brilliant Member Thank you!

Páll Márton (no activity) - 4 months, 1 week ago

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@Páll Márton (no activity) First, i didn't understand why you took 1.8, then I understood, - 1.8 + 0.18 = 1.99. Nice!! Your solution is the best!!

A Former Brilliant Member - 4 months, 1 week ago

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@Páll Márton (no activity) I put a shimmering heart emoji on it as a comment.

A Former Brilliant Member - 4 months, 1 week ago

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This is not a right way to prove, there is a way called proof by contradiction, but if from an assumption. If you haven't reached to a contradiction yet this doesn't mean that the assumption was correct. Maybe a contradiction may come out after sometime.

Zakir Husain - 4 months, 1 week ago

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My solution is bad or the Former Brilliant Member's solution is bad?

Páll Márton (no activity) - 4 months, 1 week ago

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Former Brilliant Member's solution is bad, because he wanted to explain this

Let x = 0.999.....\text{x = 0.999.....}

10x = 9.999.....\text{10x = 9.999.....}

10x = 9 + 0.999.....\text{10x = 9 + 0.999.....}

10x = 9 + x\text{10x = 9 + x}

9x = 9\text{9x = 9}

x = 1\text{x = 1}

1 = 0.999.....\text{1 = 0.999.....}

but did it in the wrong way

A Former Brilliant Member - 4 months, 1 week ago

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